Individual aspherical optical elements can be used to replace complex optical systems made up of several conventional components having spherical or plano surfaces. The reduction in the number of optical components increases transmissive efficiency and reduces cumulative errors caused by the design, fabrication, and alignment of the additional components. Specially shaped aspherical optical elements can also be used to correct spherical aberrations and other optical defects.
However, aspherical optical elements are difficult and expensive to test, especially to high accuracy. Ordinarily, interferomic inspection systems are assembled with null lenses that transform nominal spherical wavefronts into aspheric wavefronts to test aspherical optical elements. However, the null lenses present similar challenges to testing as do the aspheres themselves.
Accuracy of the null lenses is limited by manufacturing and alignment tolerances of the optical elements needed to produce the aspherical wavefront. For example, accuracies better than one-fiftieth of a wavelength of a conventional helium-neon laser are difficult to reproduce with state-of-the-art inspection systems. In addition, a unique null lens design is required for testing each different asphere.
Spherical wavefronts can be produced with much higher accuracy and can be used to measure some aspherical elements that depart only slightly from sphericity. However, when the difference between an aspherical test surface and a spherical reference surface is large, the resulting interference pattern does not accurately represent the difference in the shape between the two surfaces.
A paper entitled "Subaperture Testing of Aspheres with Annular Zones" by Ying-Moh Liu et al. of the University of Arizona proposes the combination of several subaperture measurements using spherical wavefronts into a full aperture measure of an aspherical test element. The subaperture measurements are made in successive steps by focusing the spherical wavefront in different positions along the optical axis of the aspherical test element. Each focus position produces a different interference pattern. Annular zones having well-spaced fringe patterns are defined within the interferograms for separately measuring different portions of the aspherical test element. Interferometric data reduction techniques are used to obtain polynomial coefficients describing each annular zone, and further mathematical processing is used to obtain coefficients representing the full aperture of the test element.
However, the mathematical processing requires estimates of the center and diameter of the annular zones as well as of the full aperture. Boundaries of the annular zones are determined largely by visual inspection, leading to errors in these estimates for the center and diameter. The mathematical representations of each subaperture are also sensitive to reductions in subaperture sizes, which further limits overall accuracy of the measurement. Independent graphical comparisons of phase measurements from the interferograms to a desired form of the test element are not possible.